Problem: Simplify the following expression: $t = \dfrac{q^2 + 5q - 24}{q + 8} $
Explanation: First factor the polynomial in the numerator. $ q^2 + 5q - 24 = (q + 8)(q - 3) $ So we can rewrite the expression as: $t = \dfrac{(q + 8)(q - 3)}{q + 8} $ We can divide the numerator and denominator by $(q + 8)$ on condition that $q \neq -8$ Therefore $t = q - 3; q \neq -8$